Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pH 18 2.992883
mu_beta0_pH 3 2.257721
beta1_black 13 1.983231
beta3_pH 15 1.931326
beta0_black 7 1.663816
beta1_pH 27 1.487668
beta3_yellow 9 1.480328
beta3_pelagic 9 1.422713
sd_comp 1 1.382177
beta2_yellow 5 1.350711
beta0_yellow 4 1.324306
beta2_pH 16 1.306434
parameter n badRhat_avg
beta1_pelagic 12 1.293272
beta1_yellow 7 1.288672
beta0_pelagic 10 1.280079
beta3_black 11 1.278389
beta2_pelagic 8 1.275406
mu_beta0_yellow 1 1.248655
beta_H 1 1.239398
beta2_black 6 1.189010
tau_beta0_pH 7 1.184462
tau_beta0_yellow 3 1.150473
mu_beta0_pelagic 1 1.148692
beta4_black 1 1.139800
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
beta0_black 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 0
beta0_pelagic 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1
beta0_pH 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1
beta0_yellow 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0
beta1_black 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1
beta1_pelagic 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1
beta1_pH 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1
beta1_yellow 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0
beta2_black 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0
beta2_pelagic 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0
beta2_pH 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0
beta2_yellow 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0
beta3_black 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1
beta3_pelagic 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1
beta3_pH 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0
beta3_yellow 1 0 1 1 1 0 0 0 1 1 1 1 0 0 1 0
beta4_black 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
mu_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
mu_beta0_yellow 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.138 0.069 -0.264 -0.141 0.007
mu_bc_H[2] -0.099 0.045 -0.174 -0.103 0.000
mu_bc_H[3] -0.437 0.070 -0.570 -0.438 -0.292
mu_bc_H[4] -0.986 0.189 -1.374 -0.980 -0.636
mu_bc_H[5] 0.855 0.881 -0.200 0.683 3.028
mu_bc_H[6] -2.175 0.326 -2.798 -2.188 -1.511
mu_bc_H[7] -0.454 0.109 -0.668 -0.451 -0.243
mu_bc_H[8] 0.250 0.369 -0.350 0.216 1.016
mu_bc_H[9] -0.310 0.134 -0.578 -0.309 -0.047
mu_bc_H[10] -0.114 0.069 -0.241 -0.118 0.028
mu_bc_H[11] -0.105 0.041 -0.185 -0.107 -0.021
mu_bc_H[12] -0.249 0.105 -0.468 -0.245 -0.055
mu_bc_H[13] -0.123 0.080 -0.274 -0.122 0.038
mu_bc_H[14] -0.291 0.095 -0.490 -0.290 -0.117
mu_bc_H[15] -0.346 0.053 -0.448 -0.348 -0.236
mu_bc_H[16] -0.325 0.392 -0.987 -0.354 0.543
mu_bc_R[1] 1.374 0.144 1.099 1.374 1.661
mu_bc_R[2] 1.496 0.089 1.323 1.495 1.679
mu_bc_R[3] 1.435 0.137 1.151 1.438 1.693
mu_bc_R[4] 0.954 0.200 0.519 0.968 1.305
mu_bc_R[5] 1.125 0.467 0.214 1.134 2.013
mu_bc_R[6] -1.571 0.444 -2.428 -1.562 -0.695
mu_bc_R[7] 0.368 0.215 -0.051 0.375 0.777
mu_bc_R[8] 0.542 0.195 0.161 0.543 0.915
mu_bc_R[9] 0.403 0.196 -0.039 0.419 0.751
mu_bc_R[10] 1.324 0.125 1.071 1.328 1.562
mu_bc_R[11] 1.117 0.072 0.976 1.117 1.255
mu_bc_R[12] 0.921 0.180 0.576 0.919 1.274
mu_bc_R[13] 1.062 0.093 0.878 1.062 1.242
mu_bc_R[14] 0.957 0.139 0.669 0.961 1.229
mu_bc_R[15] 0.910 0.092 0.730 0.909 1.090
mu_bc_R[16] 1.209 0.121 0.974 1.206 1.455
tau_pH[1] 2.788 0.274 2.291 2.774 3.364
tau_pH[2] 2.847 0.388 2.115 2.835 3.636
tau_pH[3] 2.852 0.430 2.083 2.825 3.788
tau_pH[4] 8.058 2.236 4.589 7.751 13.065
tau_pH[5] 4.816 1.631 2.447 4.519 8.731
beta0_pH[1,1] 0.557 0.220 0.113 0.561 0.986
beta0_pH[2,1] 1.286 0.236 0.799 1.290 1.738
beta0_pH[3,1] 1.313 0.266 0.719 1.331 1.783
beta0_pH[4,1] 1.537 0.289 0.930 1.544 2.039
beta0_pH[5,1] -0.491 0.405 -1.244 -0.483 0.371
beta0_pH[6,1] -0.306 0.459 -1.228 -0.321 0.754
beta0_pH[7,1] -0.124 0.481 -1.082 -0.140 0.737
beta0_pH[8,1] -0.555 0.285 -1.199 -0.531 -0.077
beta0_pH[9,1] -0.502 0.315 -1.254 -0.473 0.039
beta0_pH[10,1] 0.205 0.249 -0.280 0.205 0.707
beta0_pH[11,1] -0.322 0.308 -1.066 -0.280 0.184
beta0_pH[12,1] 0.485 0.284 -0.182 0.513 0.966
beta0_pH[13,1] -0.034 0.360 -0.650 -0.079 0.755
beta0_pH[14,1] -0.446 0.276 -1.021 -0.438 0.053
beta0_pH[15,1] -0.193 0.637 -1.109 -0.367 1.267
beta0_pH[16,1] 1.192 1.323 -1.104 1.947 2.571
beta0_pH[1,2] 2.548 0.224 2.113 2.556 2.968
beta0_pH[2,2] 2.797 0.250 2.198 2.837 3.177
beta0_pH[3,2] 2.452 0.242 1.967 2.462 2.900
beta0_pH[4,2] 2.523 0.295 1.891 2.581 2.958
beta0_pH[5,2] 3.899 1.173 1.957 3.747 6.701
beta0_pH[6,2] 2.797 0.280 2.247 2.802 3.321
beta0_pH[7,2] 1.878 0.255 1.337 1.910 2.233
beta0_pH[8,2] 2.700 0.415 1.450 2.782 3.107
beta0_pH[9,2] 2.707 0.579 1.609 2.670 3.640
beta0_pH[10,2] 3.625 0.253 2.998 3.660 4.020
beta0_pH[11,2] -4.875 0.296 -5.457 -4.868 -4.294
beta0_pH[12,2] -4.878 0.470 -5.967 -4.850 -4.087
beta0_pH[13,2] -4.604 0.468 -5.460 -4.629 -3.628
beta0_pH[14,2] -5.496 0.466 -6.446 -5.478 -4.675
beta0_pH[15,2] -4.238 0.348 -4.925 -4.225 -3.602
beta0_pH[16,2] -4.878 0.373 -5.641 -4.873 -4.169
beta0_pH[1,3] 1.338 0.295 0.699 1.365 1.800
beta0_pH[2,3] 1.951 0.427 0.870 2.067 2.453
beta0_pH[3,3] 2.036 0.516 0.770 2.113 2.690
beta0_pH[4,3] 2.343 0.657 0.961 2.551 3.156
beta0_pH[5,3] 0.636 1.319 -3.509 0.666 3.175
beta0_pH[6,3] 0.189 1.057 -2.050 0.447 1.917
beta0_pH[7,3] 0.299 0.993 -2.568 0.715 1.069
beta0_pH[8,3] 0.357 0.182 0.002 0.354 0.713
beta0_pH[9,3] 0.238 0.318 -0.417 0.261 0.789
beta0_pH[10,3] 0.716 0.303 0.076 0.730 1.236
beta0_pH[11,4] 1.257 1.287 -0.874 1.941 2.862
beta0_pH[12,4] 1.342 1.323 -0.733 1.936 2.980
beta0_pH[13,4] 1.081 1.113 -0.676 1.727 2.310
beta0_pH[14,4] 1.231 1.182 -0.705 1.917 2.632
beta0_pH[15,4] 1.115 1.187 -0.654 1.758 2.744
beta0_pH[16,4] 1.240 1.383 -0.667 1.837 3.367
beta0_pH[11,5] -0.787 0.232 -1.296 -0.768 -0.379
beta0_pH[12,5] -2.639 0.324 -3.224 -2.660 -1.974
beta0_pH[13,5] -0.217 0.209 -0.644 -0.209 0.172
beta0_pH[14,5] -1.017 0.234 -1.442 -1.028 -0.528
beta0_pH[15,5] -1.153 0.206 -1.581 -1.144 -0.770
beta0_pH[16,5] -1.476 1.169 -3.613 -0.797 -0.340
beta1_pH[1,1] 3.102 0.402 2.377 3.084 3.986
beta1_pH[2,1] 2.429 0.390 1.761 2.390 3.310
beta1_pH[3,1] 2.712 0.716 1.802 2.565 4.672
beta1_pH[4,1] 3.169 0.612 2.228 3.077 4.700
beta1_pH[5,1] 2.043 0.487 1.172 2.014 3.081
beta1_pH[6,1] 3.012 0.892 1.563 2.870 5.164
beta1_pH[7,1] 1.762 0.737 0.625 1.654 3.403
beta1_pH[8,1] 3.378 0.783 2.248 3.257 5.262
beta1_pH[9,1] 2.168 0.439 1.456 2.120 3.172
beta1_pH[10,1] 2.436 0.345 1.773 2.422 3.128
beta1_pH[11,1] 6.985 1.722 5.207 6.529 12.608
beta1_pH[12,1] 2.902 0.335 2.305 2.875 3.666
beta1_pH[13,1] 5.789 1.202 4.004 5.572 8.655
beta1_pH[14,1] 14.623 4.303 8.937 13.606 25.367
beta1_pH[15,1] 8.123 1.921 5.227 7.720 12.465
beta1_pH[16,1] 12.004 3.265 6.735 11.739 20.267
beta1_pH[1,2] 2.250 9.461 0.060 0.981 11.079
beta1_pH[2,2] 2.447 5.579 0.064 1.010 14.142
beta1_pH[3,2] 1.177 0.297 0.592 1.176 1.780
beta1_pH[4,2] 4.237 19.256 0.042 0.874 24.562
beta1_pH[5,2] 6.878 40.767 0.000 0.978 47.767
beta1_pH[6,2] 1.129 1.138 0.000 1.114 2.865
beta1_pH[7,2] 1.870 5.881 0.000 0.574 13.118
beta1_pH[8,2] 1.043 2.299 0.000 0.489 6.981
beta1_pH[9,2] 1.260 2.601 0.000 1.101 2.832
beta1_pH[10,2] 6.152 16.402 0.000 1.583 53.597
beta1_pH[11,2] 6.813 0.320 6.187 6.807 7.455
beta1_pH[12,2] 6.859 0.637 5.787 6.808 8.300
beta1_pH[13,2] 7.107 0.516 6.053 7.124 8.090
beta1_pH[14,2] 7.415 0.499 6.549 7.394 8.424
beta1_pH[15,2] 6.799 0.387 6.078 6.785 7.576
beta1_pH[16,2] 7.611 0.407 6.838 7.599 8.445
beta1_pH[1,3] 1.902 0.502 1.083 1.861 3.073
beta1_pH[2,3] 1.162 1.738 0.000 0.721 6.209
beta1_pH[3,3] 1.301 6.547 0.001 0.816 3.743
beta1_pH[4,3] 1.780 3.961 0.001 0.993 13.925
beta1_pH[5,3] 4.137 6.108 1.207 2.949 13.730
beta1_pH[6,3] 3.043 2.084 0.534 2.560 9.293
beta1_pH[7,3] 2.548 1.980 0.274 2.240 7.610
beta1_pH[8,3] 2.674 0.325 2.039 2.671 3.295
beta1_pH[9,3] 1.842 0.373 1.148 1.834 2.591
beta1_pH[10,3] 2.661 0.388 2.001 2.645 3.497
beta1_pH[11,4] 1.469 1.426 0.001 0.869 3.726
beta1_pH[12,4] 1.583 1.343 0.001 0.990 3.691
beta1_pH[13,4] 1.285 1.154 0.001 0.767 3.201
beta1_pH[14,4] 1.845 5.675 0.001 0.867 3.351
beta1_pH[15,4] 1.315 1.173 0.001 0.898 3.302
beta1_pH[16,4] 1.597 1.626 0.001 1.357 3.706
beta1_pH[11,5] 8.035 16.985 1.501 3.346 31.573
beta1_pH[12,5] 18.232 22.651 3.399 10.619 83.297
beta1_pH[13,5] 27.263 53.258 2.982 10.483 172.244
beta1_pH[14,5] 42.956 158.292 1.666 8.368 436.584
beta1_pH[15,5] 12.499 11.555 1.783 7.967 39.697
beta1_pH[16,5] 15.915 16.745 1.878 8.165 56.562
beta2_pH[1,1] 0.501 0.240 0.260 0.465 0.946
beta2_pH[2,1] 0.520 0.346 0.188 0.449 1.270
beta2_pH[3,1] 0.441 0.333 0.139 0.381 1.087
beta2_pH[4,1] 0.367 0.170 0.161 0.335 0.778
beta2_pH[5,1] 0.705 0.759 0.150 0.475 2.621
beta2_pH[6,1] 0.332 0.462 0.118 0.244 0.980
beta2_pH[7,1] 0.355 0.712 -0.007 0.135 1.972
beta2_pH[8,1] 0.332 0.237 0.152 0.293 0.709
beta2_pH[9,1] 0.513 0.361 0.175 0.434 1.340
beta2_pH[10,1] 0.568 0.359 0.229 0.493 1.382
beta2_pH[11,1] 0.235 0.065 0.113 0.233 0.373
beta2_pH[12,1] 1.117 0.596 0.427 0.995 2.575
beta2_pH[13,1] 0.261 0.072 0.157 0.251 0.435
beta2_pH[14,1] 0.249 0.042 0.177 0.245 0.344
beta2_pH[15,1] 0.208 0.052 0.133 0.202 0.334
beta2_pH[16,1] 0.547 0.428 0.136 0.522 1.486
beta2_pH[1,2] 1.450 6.089 -11.365 1.547 14.007
beta2_pH[2,2] -3.969 5.461 -16.549 -3.188 7.180
beta2_pH[3,2] -5.401 4.247 -16.179 -4.209 -0.722
beta2_pH[4,2] -5.118 5.142 -16.923 -4.160 3.799
beta2_pH[5,2] -1.090 6.187 -13.341 -1.431 12.458
beta2_pH[6,2] -4.113 5.466 -16.273 -3.675 7.646
beta2_pH[7,2] -3.616 5.662 -15.390 -3.440 8.893
beta2_pH[8,2] -2.574 6.235 -15.083 -2.889 11.084
beta2_pH[9,2] -4.381 5.272 -15.421 -3.963 7.531
beta2_pH[10,2] -5.041 5.527 -17.484 -4.434 6.391
beta2_pH[11,2] -8.063 3.728 -17.734 -7.212 -3.587
beta2_pH[12,2] -2.431 2.574 -9.865 -1.297 -0.513
beta2_pH[13,2] -3.605 2.594 -10.896 -2.762 -1.358
beta2_pH[14,2] -5.162 3.149 -13.530 -4.248 -1.824
beta2_pH[15,2] -7.834 3.918 -18.195 -6.749 -3.439
beta2_pH[16,2] -8.297 3.897 -18.773 -7.370 -3.686
beta2_pH[1,3] 4.508 4.102 0.334 3.320 16.038
beta2_pH[2,3] 1.759 5.636 -10.631 1.479 13.958
beta2_pH[3,3] 0.172 6.167 -13.354 0.429 12.492
beta2_pH[4,3] 1.269 5.085 -10.443 1.264 12.491
beta2_pH[5,3] 4.614 5.913 -8.629 4.450 17.152
beta2_pH[6,3] 5.667 6.185 -5.813 4.941 21.379
beta2_pH[7,3] 3.082 6.439 -10.585 3.604 15.971
beta2_pH[8,3] 8.392 4.564 2.510 7.380 20.039
beta2_pH[9,3] 6.599 4.169 1.537 5.592 17.335
beta2_pH[10,3] 5.402 4.313 0.554 4.498 16.614
beta2_pH[11,4] -2.957 5.777 -15.117 -2.430 10.754
beta2_pH[12,4] -3.392 5.612 -15.879 -2.762 9.147
beta2_pH[13,4] 0.116 5.600 -12.446 0.932 11.714
beta2_pH[14,4] -1.975 6.899 -12.694 -2.408 15.414
beta2_pH[15,4] 0.120 5.789 -12.546 1.061 12.164
beta2_pH[16,4] 1.565 6.930 -12.935 1.985 14.927
beta2_pH[11,5] -2.919 2.495 -9.746 -2.277 -0.429
beta2_pH[12,5] -3.833 3.034 -12.329 -2.919 -0.849
beta2_pH[13,5] -3.551 2.578 -11.042 -2.772 -1.033
beta2_pH[14,5] -4.111 2.662 -11.431 -3.438 -1.099
beta2_pH[15,5] -4.081 2.755 -11.066 -3.217 -0.889
beta2_pH[16,5] -1.397 3.402 -8.662 -1.783 4.977
beta3_pH[1,1] 35.807 1.084 33.807 35.737 38.111
beta3_pH[2,1] 34.098 1.624 31.350 33.913 37.927
beta3_pH[3,1] 35.711 2.189 32.340 35.424 41.447
beta3_pH[4,1] 35.878 1.822 32.830 35.696 39.988
beta3_pH[5,1] 29.633 2.860 25.913 29.019 36.185
beta3_pH[6,1] 38.601 3.417 32.228 38.600 44.872
beta3_pH[7,1] 32.884 8.614 18.817 32.676 45.717
beta3_pH[8,1] 39.022 2.110 34.786 39.040 43.503
beta3_pH[9,1] 31.269 2.052 27.882 31.080 35.884
beta3_pH[10,1] 32.814 1.277 30.580 32.724 35.478
beta3_pH[11,1] 35.960 2.319 33.218 35.424 43.796
beta3_pH[12,1] 30.416 0.591 29.106 30.451 31.482
beta3_pH[13,1] 38.799 2.129 35.252 38.521 43.627
beta3_pH[14,1] 41.309 2.057 37.922 41.031 45.547
beta3_pH[15,1] 40.248 2.537 35.975 39.909 45.403
beta3_pH[16,1] 44.263 1.382 40.597 44.510 45.912
beta3_pH[1,2] 36.027 8.180 18.985 40.376 44.445
beta3_pH[2,2] 30.009 6.564 18.830 29.116 43.780
beta3_pH[3,2] 41.759 1.459 39.925 41.840 43.776
beta3_pH[4,2] 33.249 9.204 18.926 37.914 45.109
beta3_pH[5,2] 30.508 8.024 18.487 29.797 45.087
beta3_pH[6,2] 33.910 5.530 19.398 35.438 44.302
beta3_pH[7,2] 28.211 7.342 18.364 26.977 44.626
beta3_pH[8,2] 28.687 7.291 18.465 27.389 43.853
beta3_pH[9,2] 39.439 8.264 19.270 43.854 45.804
beta3_pH[10,2] 30.246 5.717 19.232 29.851 42.139
beta3_pH[11,2] 43.349 0.158 43.105 43.329 43.697
beta3_pH[12,2] 43.088 0.282 42.439 43.117 43.612
beta3_pH[13,2] 43.803 0.142 43.502 43.817 44.044
beta3_pH[14,2] 43.293 0.154 43.056 43.277 43.637
beta3_pH[15,2] 43.386 0.168 43.119 43.363 43.759
beta3_pH[16,2] 43.485 0.173 43.172 43.481 43.826
beta3_pH[1,3] 39.989 0.988 37.330 40.073 41.367
beta3_pH[2,3] 47.811 58.570 1.541 38.300 172.127
beta3_pH[3,3] 96.837 157.656 4.812 41.708 630.523
beta3_pH[4,3] 50.500 52.289 1.045 35.328 171.212
beta3_pH[5,3] 31.848 20.013 8.813 28.155 77.498
beta3_pH[6,3] 33.694 13.966 10.738 32.168 67.692
beta3_pH[7,3] 44.675 35.701 12.923 35.011 120.699
beta3_pH[8,3] 41.504 0.221 41.113 41.501 41.922
beta3_pH[9,3] 33.869 0.516 33.015 33.861 34.925
beta3_pH[10,3] 35.995 0.585 34.413 36.072 36.854
beta3_pH[11,4] 54.607 13.341 41.313 47.562 85.080
beta3_pH[12,4] 49.281 31.131 13.464 42.198 126.618
beta3_pH[13,4] 42.172 13.102 29.552 35.822 67.391
beta3_pH[14,4] 40.087 10.679 17.538 41.516 62.709
beta3_pH[15,4] 37.985 19.901 7.221 30.750 85.962
beta3_pH[16,4] 43.888 38.021 14.657 34.257 173.188
beta3_pH[11,5] 39.804 1.224 36.665 39.952 41.820
beta3_pH[12,5] 38.358 1.407 35.698 38.415 41.635
beta3_pH[13,5] 40.294 0.850 38.143 40.426 41.639
beta3_pH[14,5] 39.416 1.115 36.962 39.380 42.095
beta3_pH[15,5] 40.179 0.857 37.751 40.362 41.361
beta3_pH[16,5] 35.611 4.672 27.917 38.149 40.613
beta0_pelagic[1] 1.333 0.840 -0.220 1.455 2.393
beta0_pelagic[2] 0.848 0.688 -0.676 0.984 1.698
beta0_pelagic[3] 0.294 0.298 -0.336 0.303 0.843
beta0_pelagic[4] 0.156 0.557 -1.257 0.260 1.056
beta0_pelagic[5] -5.276 2.105 -10.384 -4.918 -2.151
beta0_pelagic[6] 1.306 1.009 -1.842 1.557 1.852
beta0_pelagic[7] 1.499 0.202 1.018 1.522 1.790
beta0_pelagic[8] 1.841 0.191 1.445 1.859 2.124
beta0_pelagic[9] 0.000 4.636 -12.799 1.979 2.876
beta0_pelagic[10] 2.551 0.288 1.820 2.592 2.844
beta0_pelagic[11] 0.693 0.126 0.442 0.698 0.938
beta0_pelagic[12] 1.753 0.137 1.486 1.754 2.019
beta0_pelagic[13] 0.555 0.156 0.222 0.560 0.849
beta0_pelagic[14] 0.376 0.183 0.000 0.381 0.714
beta0_pelagic[15] -0.233 0.127 -0.465 -0.239 0.038
beta0_pelagic[16] 0.528 0.147 0.224 0.531 0.799
beta1_pelagic[1] 0.964 0.827 0.000 0.883 2.518
beta1_pelagic[2] 0.741 0.679 0.000 0.667 2.190
beta1_pelagic[3] 0.801 0.406 0.000 0.780 1.724
beta1_pelagic[4] 1.049 0.605 0.000 0.967 2.547
beta1_pelagic[5] 6.876 2.112 3.740 6.513 12.016
beta1_pelagic[6] 1.080 2.682 0.000 0.004 9.900
beta1_pelagic[7] 0.906 2.751 0.000 0.002 9.551
beta1_pelagic[8] 1.085 3.565 0.000 0.002 14.407
beta1_pelagic[9] 2.900 4.675 0.000 1.020 15.768
beta1_pelagic[10] 0.577 1.866 0.000 0.001 7.634
beta1_pelagic[11] 2.324 0.239 1.881 2.320 2.815
beta1_pelagic[12] 2.628 0.277 2.085 2.630 3.184
beta1_pelagic[13] 2.332 0.629 1.507 2.194 3.900
beta1_pelagic[14] 3.651 1.153 2.185 3.407 7.227
beta1_pelagic[15] 2.510 0.238 2.061 2.505 2.966
beta1_pelagic[16] 3.090 0.361 2.513 3.048 4.015
beta2_pelagic[1] 0.131 4.530 -9.966 0.336 9.630
beta2_pelagic[2] 1.213 4.550 -8.792 1.070 10.500
beta2_pelagic[3] 2.338 3.477 -1.504 1.159 11.895
beta2_pelagic[4] 1.838 2.680 -0.229 1.129 9.052
beta2_pelagic[5] -9.960 4.619 -21.579 -9.153 -3.693
beta2_pelagic[6] -1.597 6.625 -14.831 -2.497 13.703
beta2_pelagic[7] -1.776 7.617 -16.281 -2.114 14.618
beta2_pelagic[8] -2.161 7.233 -16.357 -2.518 13.643
beta2_pelagic[9] 2.066 6.029 -10.933 0.780 15.790
beta2_pelagic[10] -1.064 6.643 -16.229 -0.514 13.379
beta2_pelagic[11] 7.964 4.440 1.645 7.459 16.481
beta2_pelagic[12] 8.140 4.573 2.119 7.143 19.670
beta2_pelagic[13] 2.180 3.117 0.289 0.882 11.366
beta2_pelagic[14] 0.543 0.702 0.208 0.395 1.733
beta2_pelagic[15] 8.190 4.438 2.545 7.075 19.208
beta2_pelagic[16] 5.784 4.546 0.461 4.632 17.282
beta3_pelagic[1] 76.372 72.697 3.496 47.135 257.450
beta3_pelagic[2] 27.537 16.967 2.136 22.477 62.224
beta3_pelagic[3] 29.495 6.860 18.189 29.402 43.114
beta3_pelagic[4] 24.631 4.105 15.525 24.819 33.423
beta3_pelagic[5] 46.557 0.192 46.205 46.561 46.905
beta3_pelagic[6] 60.099 85.173 1.612 37.301 387.610
beta3_pelagic[7] 63.468 94.998 1.860 33.891 413.855
beta3_pelagic[8] 45.431 74.943 1.993 27.025 243.763
beta3_pelagic[9] 27.143 13.499 2.830 25.770 59.579
beta3_pelagic[10] 57.864 95.832 1.122 32.586 399.347
beta3_pelagic[11] 43.290 0.286 42.791 43.246 43.847
beta3_pelagic[12] 43.463 0.238 43.057 43.446 43.904
beta3_pelagic[13] 42.908 1.139 40.844 42.878 45.483
beta3_pelagic[14] 43.582 1.650 40.360 43.420 47.889
beta3_pelagic[15] 43.275 0.214 42.898 43.250 43.732
beta3_pelagic[16] 43.218 0.321 42.401 43.232 43.754
mu_beta0_pelagic[1] 0.627 0.672 -0.583 0.568 2.004
mu_beta0_pelagic[2] 0.371 1.531 -3.141 0.546 3.049
mu_beta0_pelagic[3] 0.596 0.346 -0.074 0.600 1.266
tau_beta0_pelagic[1] 14.821 38.258 0.125 2.225 126.582
tau_beta0_pelagic[2] 0.139 0.143 0.011 0.097 0.495
tau_beta0_pelagic[3] 2.385 1.605 0.372 2.042 6.327
beta0_yellow[1] -0.575 0.281 -1.344 -0.523 -0.227
beta0_yellow[2] 0.488 0.161 0.131 0.498 0.769
beta0_yellow[3] -0.304 0.194 -0.695 -0.292 0.041
beta0_yellow[4] 0.762 0.295 -0.047 0.813 1.162
beta0_yellow[5] -1.088 0.423 -1.919 -1.087 -0.242
beta0_yellow[6] 0.257 0.209 -0.140 0.252 0.680
beta0_yellow[7] 0.292 0.838 -1.434 0.454 1.321
beta0_yellow[8] 0.403 0.751 -1.326 0.758 1.240
beta0_yellow[9] -0.048 0.253 -0.522 -0.057 0.490
beta0_yellow[10] 0.236 0.150 -0.050 0.237 0.527
beta0_yellow[11] -2.139 0.539 -3.264 -2.110 -1.146
beta0_yellow[12] -3.449 0.441 -4.399 -3.436 -2.639
beta0_yellow[13] -3.325 0.584 -4.345 -3.383 -1.974
beta0_yellow[14] -2.170 0.730 -3.567 -2.177 -0.349
beta0_yellow[15] -2.897 0.461 -3.816 -2.868 -2.063
beta0_yellow[16] -2.405 0.492 -3.408 -2.396 -1.480
beta1_yellow[1] 0.594 0.733 0.000 0.469 2.106
beta1_yellow[2] 1.076 0.336 0.581 1.036 1.975
beta1_yellow[3] 0.666 0.297 0.016 0.657 1.239
beta1_yellow[4] 1.712 1.643 0.685 1.265 6.174
beta1_yellow[5] 2.754 1.727 1.192 2.588 4.622
beta1_yellow[6] 2.227 0.342 1.571 2.219 2.876
beta1_yellow[7] 1.867 1.477 0.061 1.588 5.813
beta1_yellow[8] 1.791 1.872 0.115 1.513 5.085
beta1_yellow[9] 1.496 0.393 0.832 1.487 2.147
beta1_yellow[10] 2.544 0.472 1.702 2.519 3.517
beta1_yellow[11] 2.271 0.535 1.319 2.255 3.387
beta1_yellow[12] 2.240 0.461 1.385 2.224 3.185
beta1_yellow[13] 2.467 0.662 0.939 2.587 3.549
beta1_yellow[14] 2.239 0.659 0.927 2.197 3.643
beta1_yellow[15] 2.182 0.466 1.357 2.148 3.144
beta1_yellow[16] 2.212 0.502 1.264 2.191 3.261
beta2_yellow[1] -2.321 4.625 -12.765 -1.618 7.600
beta2_yellow[2] -3.545 3.673 -13.668 -2.319 -0.184
beta2_yellow[3] -3.463 3.643 -13.299 -2.341 -0.130
beta2_yellow[4] -2.254 3.277 -11.817 -0.853 -0.078
beta2_yellow[5] -6.895 4.942 -19.373 -5.674 -0.700
beta2_yellow[6] 6.440 4.665 1.179 5.253 18.323
beta2_yellow[7] 0.125 7.787 -15.466 0.226 15.515
beta2_yellow[8] -1.289 7.357 -16.270 -0.988 14.657
beta2_yellow[9] 6.902 5.006 0.592 5.865 18.942
beta2_yellow[10] -7.294 4.735 -19.355 -6.248 -1.206
beta2_yellow[11] -4.023 3.189 -12.956 -3.069 -0.829
beta2_yellow[12] -4.408 3.195 -13.225 -3.476 -0.977
beta2_yellow[13] -1.293 5.415 -8.724 -2.569 13.610
beta2_yellow[14] -4.177 3.550 -14.064 -3.173 -0.240
beta2_yellow[15] -4.000 2.893 -11.905 -3.151 -0.955
beta2_yellow[16] -4.662 3.473 -14.300 -3.691 -1.056
beta3_yellow[1] 48.516 44.277 10.147 30.789 157.854
beta3_yellow[2] 29.206 1.580 25.843 28.993 32.416
beta3_yellow[3] 33.233 8.405 25.409 32.836 41.046
beta3_yellow[4] 28.728 5.155 13.319 28.549 35.902
beta3_yellow[5] 33.497 2.999 31.327 33.450 36.096
beta3_yellow[6] 39.584 0.468 38.791 39.557 40.653
beta3_yellow[7] 35.437 23.368 12.037 27.879 116.209
beta3_yellow[8] 40.221 35.056 13.031 29.418 108.641
beta3_yellow[9] 37.541 2.097 36.277 37.570 41.959
beta3_yellow[10] 29.420 0.384 28.488 29.452 29.971
beta3_yellow[11] 45.848 0.895 44.439 45.831 47.232
beta3_yellow[12] 43.392 0.508 42.400 43.351 44.525
beta3_yellow[13] 39.751 8.561 20.816 44.695 45.459
beta3_yellow[14] 45.532 5.226 33.107 45.157 55.410
beta3_yellow[15] 45.490 0.613 44.233 45.564 46.522
beta3_yellow[16] 45.379 3.779 43.417 44.688 58.370
mu_beta0_yellow[1] 0.079 0.443 -0.856 0.088 0.958
mu_beta0_yellow[2] -0.003 0.416 -0.851 0.001 0.810
mu_beta0_yellow[3] -2.549 0.562 -3.512 -2.597 -1.275
tau_beta0_yellow[1] 2.861 4.147 0.195 1.925 10.430
tau_beta0_yellow[2] 3.416 10.026 0.305 1.745 14.848
tau_beta0_yellow[3] 5.128 17.023 0.229 1.815 28.731
beta0_black[1] 0.104 0.188 -0.291 0.117 0.429
beta0_black[2] 1.770 0.370 0.639 1.869 2.142
beta0_black[3] 1.175 0.316 0.336 1.269 1.552
beta0_black[4] 2.269 0.265 1.706 2.329 2.636
beta0_black[5] 1.637 1.524 -1.246 1.684 4.318
beta0_black[6] 1.658 1.482 -1.241 1.671 4.590
beta0_black[7] 1.614 1.570 -1.255 1.660 4.382
beta0_black[8] 1.297 0.219 0.885 1.297 1.720
beta0_black[9] 2.370 0.287 1.813 2.373 2.877
beta0_black[10] 1.471 0.129 1.224 1.468 1.722
beta0_black[11] 3.398 0.260 2.656 3.433 3.736
beta0_black[12] 4.601 0.245 4.164 4.587 5.086
beta0_black[13] -0.081 0.210 -0.486 -0.080 0.329
beta0_black[14] 2.206 0.485 0.863 2.298 2.845
beta0_black[15] 1.211 0.255 0.572 1.252 1.562
beta0_black[16] 4.099 0.455 2.742 4.215 4.535
beta2_black[1] 1.862 6.487 -12.355 2.104 15.023
beta2_black[2] 0.870 5.344 -11.358 1.328 12.038
beta2_black[3] 0.328 6.496 -13.011 0.394 13.778
beta2_black[4] -1.361 6.042 -14.012 -1.301 11.422
beta2_black[5] -0.119 6.617 -13.798 -0.036 13.512
beta2_black[6] -0.020 6.806 -14.283 -0.107 14.157
beta2_black[7] 0.056 6.616 -13.278 0.047 14.068
beta2_black[8] -0.062 6.602 -13.290 -0.056 13.372
beta2_black[9] -0.303 6.518 -13.703 -0.126 13.470
beta2_black[10] -0.044 6.680 -13.807 -0.106 14.008
beta2_black[11] -3.219 4.244 -11.877 -2.767 6.047
beta2_black[12] -3.554 4.201 -13.113 -2.918 5.285
beta2_black[13] -3.590 3.333 -12.375 -2.382 -0.553
beta2_black[14] -2.936 3.605 -13.199 -1.472 -0.112
beta2_black[15] -2.867 4.578 -13.385 -2.252 6.312
beta2_black[16] -3.349 5.156 -14.695 -2.255 6.010
beta3_black[1] 130.859 376.682 0.080 41.510 1067.765
beta3_black[2] 158.223 510.875 0.107 27.493 1501.601
beta3_black[3] 108.706 246.060 0.076 29.138 882.060
beta3_black[4] 830.340 1464.981 0.758 35.571 4880.881
beta3_black[5] 26646.434 817331.659 0.085 33.016 13116.030
beta3_black[6] 10881.294 232487.958 0.104 30.723 11317.766
beta3_black[7] 16910.256 465615.372 0.073 31.671 8377.820
beta3_black[8] 266.222 829.009 0.078 30.575 3175.733
beta3_black[9] 200.187 592.884 0.107 29.469 1992.038
beta3_black[10] 99.428 262.176 0.069 26.431 836.849
beta3_black[11] 40.289 25.765 14.680 35.675 94.284
beta3_black[12] 39.429 54.079 19.202 33.134 78.683
beta3_black[13] 39.331 0.636 37.842 39.376 40.387
beta3_black[14] 38.416 5.001 29.839 38.814 45.587
beta3_black[15] 43.277 49.357 15.209 37.181 98.469
beta3_black[16] 42.697 50.793 11.649 36.993 95.788
beta4_black[1] -0.279 0.185 -0.644 -0.279 0.073
beta4_black[2] 0.252 0.178 -0.099 0.251 0.597
beta4_black[3] -0.935 0.186 -1.291 -0.936 -0.564
beta4_black[4] 0.466 0.222 0.050 0.465 0.917
beta4_black[5] 0.313 2.580 -4.549 0.212 5.644
beta4_black[6] 0.179 2.946 -4.840 0.179 5.167
beta4_black[7] 0.251 2.338 -4.608 0.183 4.863
beta4_black[8] -0.717 0.364 -1.450 -0.712 -0.004
beta4_black[9] 1.578 1.047 -0.057 1.462 3.951
beta4_black[10] 0.021 0.177 -0.330 0.023 0.371
beta4_black[11] -0.688 0.201 -1.098 -0.688 -0.296
beta4_black[12] 0.272 0.324 -0.358 0.267 0.907
beta4_black[13] -1.193 0.211 -1.614 -1.192 -0.774
beta4_black[14] -0.125 0.226 -0.561 -0.128 0.324
beta4_black[15] -0.892 0.205 -1.298 -0.892 -0.487
beta4_black[16] -0.597 0.218 -1.034 -0.593 -0.176
mu_beta0_black[1] 1.257 0.712 -0.264 1.294 2.575
mu_beta0_black[2] 1.638 0.664 0.081 1.683 2.860
mu_beta0_black[3] 2.370 0.910 0.399 2.422 4.055
tau_beta0_black[1] 1.154 1.005 0.090 0.879 3.655
tau_beta0_black[2] 4.199 9.695 0.076 2.044 20.121
tau_beta0_black[3] 0.307 0.198 0.051 0.265 0.809
beta0_dsr[11] -3.009 0.273 -3.556 -3.008 -2.451
beta0_dsr[12] 3.981 1.769 -2.706 4.425 4.999
beta0_dsr[13] -1.713 0.454 -3.114 -1.646 -1.079
beta0_dsr[14] -4.295 0.484 -5.181 -4.308 -3.329
beta0_dsr[15] -2.410 0.266 -2.945 -2.411 -1.875
beta0_dsr[16] -3.077 0.362 -3.789 -3.075 -2.375
beta1_dsr[11] 4.883 0.283 4.317 4.880 5.434
beta1_dsr[12] 6.083 3.563 2.486 5.272 15.232
beta1_dsr[13] 3.199 0.558 2.547 3.096 5.175
beta1_dsr[14] 6.924 0.513 5.954 6.933 7.901
beta1_dsr[15] 3.606 0.273 3.067 3.606 4.143
beta1_dsr[16] 5.859 0.378 5.111 5.861 6.593
beta2_dsr[11] -9.513 3.902 -19.712 -8.534 -4.936
beta2_dsr[12] -7.779 4.139 -18.795 -6.900 -2.166
beta2_dsr[13] -5.470 3.257 -13.053 -5.309 -0.340
beta2_dsr[14] -6.711 3.034 -14.563 -6.063 -2.595
beta2_dsr[15] -7.847 3.679 -17.689 -6.600 -3.893
beta2_dsr[16] -9.161 4.061 -20.003 -8.060 -4.425
beta3_dsr[11] 43.482 0.153 43.201 43.476 43.781
beta3_dsr[12] 35.361 4.818 32.646 34.260 51.799
beta3_dsr[13] 43.263 0.353 42.767 43.201 43.947
beta3_dsr[14] 43.265 0.135 43.077 43.240 43.606
beta3_dsr[15] 43.462 0.184 43.144 43.452 43.835
beta3_dsr[16] 43.432 0.166 43.150 43.417 43.776
beta4_dsr[11] 0.663 0.208 0.248 0.666 1.080
beta4_dsr[12] 0.321 0.460 -0.618 0.318 1.197
beta4_dsr[13] -0.069 0.215 -0.503 -0.064 0.335
beta4_dsr[14] 0.207 0.249 -0.289 0.210 0.678
beta4_dsr[15] 0.983 0.213 0.569 0.983 1.411
beta4_dsr[16] 0.176 0.221 -0.273 0.174 0.606
beta0_slope[11] -1.994 0.162 -2.316 -1.991 -1.673
beta0_slope[12] -4.635 0.273 -5.185 -4.627 -4.131
beta0_slope[13] -1.447 0.216 -1.960 -1.425 -1.096
beta0_slope[14] -2.763 0.178 -3.114 -2.762 -2.416
beta0_slope[15] -1.725 0.157 -2.034 -1.723 -1.425
beta0_slope[16] -2.736 0.170 -3.054 -2.739 -2.396
beta1_slope[11] 4.374 0.293 3.805 4.372 4.949
beta1_slope[12] 4.810 0.539 3.778 4.811 5.909
beta1_slope[13] 2.738 0.524 2.036 2.643 4.364
beta1_slope[14] 5.341 0.688 4.198 5.255 6.838
beta1_slope[15] 2.079 0.282 1.529 2.083 2.628
beta1_slope[16] 5.269 0.390 4.540 5.268 6.062
beta2_slope[11] 9.789 3.727 4.445 9.264 18.327
beta2_slope[12] 6.831 4.124 1.486 5.961 17.712
beta2_slope[13] 4.234 3.369 0.319 3.420 12.680
beta2_slope[14] 1.518 0.733 0.829 1.367 2.964
beta2_slope[15] 7.148 3.933 2.389 6.140 17.819
beta2_slope[16] 8.714 4.038 3.462 7.875 19.476
beta3_slope[11] 43.526 0.152 43.224 43.531 43.794
beta3_slope[12] 43.449 0.210 43.044 43.465 43.822
beta3_slope[13] 43.589 0.296 43.046 43.585 44.116
beta3_slope[14] 43.893 0.392 43.340 43.809 44.830
beta3_slope[15] 43.594 0.192 43.218 43.594 43.967
beta3_slope[16] 43.511 0.162 43.203 43.517 43.814
beta4_slope[11] -0.461 0.215 -0.896 -0.459 -0.037
beta4_slope[12] -1.238 0.669 -2.758 -1.141 -0.226
beta4_slope[13] 0.179 0.211 -0.233 0.174 0.608
beta4_slope[14] -0.066 0.241 -0.549 -0.064 0.393
beta4_slope[15] -0.188 0.202 -0.585 -0.189 0.216
beta4_slope[16] -0.150 0.228 -0.604 -0.147 0.290
sigma_H[1] 0.199 0.053 0.104 0.197 0.315
sigma_H[2] 0.171 0.030 0.117 0.169 0.238
sigma_H[3] 0.196 0.043 0.120 0.193 0.288
sigma_H[4] 0.421 0.077 0.293 0.415 0.592
sigma_H[5] 0.983 0.212 0.600 0.975 1.413
sigma_H[6] 0.379 0.201 0.026 0.374 0.796
sigma_H[7] 0.314 0.068 0.209 0.304 0.484
sigma_H[8] 0.424 0.096 0.258 0.417 0.625
sigma_H[9] 0.509 0.119 0.326 0.493 0.789
sigma_H[10] 0.217 0.043 0.143 0.213 0.314
sigma_H[11] 0.276 0.045 0.200 0.272 0.382
sigma_H[12] 0.443 0.162 0.211 0.423 0.754
sigma_H[13] 0.215 0.038 0.148 0.211 0.296
sigma_H[14] 0.509 0.094 0.345 0.500 0.715
sigma_H[15] 0.252 0.041 0.182 0.247 0.344
sigma_H[16] 0.228 0.043 0.154 0.224 0.328
lambda_H[1] 3.068 4.160 0.174 1.734 14.190
lambda_H[2] 8.371 7.608 0.857 6.261 29.249
lambda_H[3] 6.277 9.702 0.269 3.075 31.935
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.623 7.310 0.026 0.936 25.566
lambda_H[6] 7.899 16.641 0.008 0.710 51.503
lambda_H[7] 0.012 0.008 0.002 0.010 0.034
lambda_H[8] 8.261 10.333 0.051 4.722 36.017
lambda_H[9] 0.016 0.011 0.003 0.013 0.044
lambda_H[10] 0.323 0.805 0.030 0.202 1.192
lambda_H[11] 0.246 0.360 0.012 0.130 1.149
lambda_H[12] 4.887 5.976 0.207 2.912 21.578
lambda_H[13] 3.352 3.090 0.263 2.488 11.506
lambda_H[14] 3.665 4.736 0.226 2.187 16.886
lambda_H[15] 0.027 0.040 0.003 0.017 0.115
lambda_H[16] 1.678 2.356 0.077 0.940 7.603
mu_lambda_H[1] 4.356 1.900 1.242 4.190 8.464
mu_lambda_H[2] 3.787 1.938 0.562 3.594 7.828
mu_lambda_H[3] 3.554 1.835 0.799 3.298 7.613
sigma_lambda_H[1] 8.652 4.249 2.092 8.108 18.069
sigma_lambda_H[2] 8.358 4.714 0.942 7.698 18.323
sigma_lambda_H[3] 6.178 3.870 1.036 5.378 15.591
beta_H[1,1] 6.899 1.053 4.293 7.065 8.462
beta_H[2,1] 9.871 0.483 8.848 9.890 10.774
beta_H[3,1] 8.005 0.793 6.188 8.102 9.326
beta_H[4,1] 9.392 7.816 -6.823 9.663 24.384
beta_H[5,1] 0.136 2.456 -4.981 0.299 4.265
beta_H[6,1] 2.950 4.106 -7.241 4.525 7.522
beta_H[7,1] 0.028 6.024 -13.293 0.407 10.736
beta_H[8,1] 1.705 5.275 -2.377 1.266 4.134
beta_H[9,1] 13.140 5.608 1.838 12.899 24.561
beta_H[10,1] 7.089 1.729 3.428 7.181 10.344
beta_H[11,1] 5.229 3.360 -2.415 5.804 10.011
beta_H[12,1] 2.585 1.027 0.734 2.519 4.865
beta_H[13,1] 9.062 0.885 7.284 9.111 10.591
beta_H[14,1] 2.215 1.050 0.163 2.233 4.202
beta_H[15,1] -5.791 3.945 -13.076 -6.080 2.805
beta_H[16,1] 3.076 2.104 -0.646 2.913 8.069
beta_H[1,2] 7.915 0.243 7.420 7.920 8.388
beta_H[2,2] 10.026 0.134 9.760 10.028 10.286
beta_H[3,2] 8.953 0.201 8.569 8.950 9.361
beta_H[4,2] 3.521 1.464 0.829 3.443 6.639
beta_H[5,2] 1.984 0.950 0.106 2.003 3.727
beta_H[6,2] 5.704 1.093 3.180 5.895 7.329
beta_H[7,2] 2.795 1.139 0.739 2.731 5.247
beta_H[8,2] 2.930 1.388 1.066 3.140 4.284
beta_H[9,2] 3.366 1.099 1.289 3.362 5.582
beta_H[10,2] 8.179 0.347 7.489 8.182 8.816
beta_H[11,2] 9.719 0.605 8.807 9.610 11.075
beta_H[12,2] 3.932 0.357 3.264 3.933 4.672
beta_H[13,2] 9.111 0.256 8.649 9.100 9.618
beta_H[14,2] 4.025 0.355 3.353 4.010 4.759
beta_H[15,2] 11.308 0.709 9.843 11.329 12.665
beta_H[16,2] 4.675 0.781 3.139 4.694 6.184
beta_H[1,3] 8.496 0.246 8.067 8.480 9.020
beta_H[2,3] 10.078 0.117 9.850 10.078 10.316
beta_H[3,3] 9.614 0.162 9.298 9.610 9.955
beta_H[4,3] -2.469 0.880 -4.260 -2.458 -0.774
beta_H[5,3] 3.904 0.632 2.621 3.927 5.140
beta_H[6,3] 8.131 1.243 6.435 7.723 10.819
beta_H[7,3] -2.915 0.698 -4.315 -2.896 -1.588
beta_H[8,3] 5.281 0.632 4.609 5.179 6.637
beta_H[9,3] -2.651 0.747 -4.119 -2.632 -1.181
beta_H[10,3] 8.734 0.278 8.178 8.735 9.290
beta_H[11,3] 8.547 0.276 7.950 8.566 9.035
beta_H[12,3] 5.259 0.312 4.553 5.297 5.778
beta_H[13,3] 8.827 0.175 8.477 8.829 9.159
beta_H[14,3] 5.691 0.279 5.094 5.709 6.175
beta_H[15,3] 10.391 0.331 9.749 10.397 11.020
beta_H[16,3] 6.636 0.541 5.340 6.704 7.506
beta_H[1,4] 8.282 0.176 7.906 8.295 8.592
beta_H[2,4] 10.139 0.118 9.882 10.149 10.353
beta_H[3,4] 10.123 0.163 9.767 10.136 10.415
beta_H[4,4] 11.767 0.448 10.872 11.775 12.632
beta_H[5,4] 5.589 0.785 4.299 5.503 7.417
beta_H[6,4] 7.033 0.958 4.877 7.330 8.313
beta_H[7,4] 8.302 0.362 7.560 8.313 8.999
beta_H[8,4] 6.689 0.287 6.134 6.707 7.148
beta_H[9,4] 7.191 0.465 6.317 7.189 8.090
beta_H[10,4] 7.758 0.244 7.303 7.747 8.256
beta_H[11,4] 9.292 0.201 8.902 9.294 9.701
beta_H[12,4] 7.124 0.213 6.711 7.118 7.564
beta_H[13,4] 9.009 0.144 8.725 9.012 9.285
beta_H[14,4] 7.671 0.215 7.257 7.673 8.090
beta_H[15,4] 9.445 0.243 8.982 9.442 9.933
beta_H[16,4] 9.168 0.211 8.804 9.148 9.625
beta_H[1,5] 8.978 0.148 8.674 8.982 9.269
beta_H[2,5] 10.780 0.092 10.601 10.778 10.972
beta_H[3,5] 10.925 0.173 10.609 10.918 11.286
beta_H[4,5] 8.395 0.469 7.528 8.385 9.350
beta_H[5,5] 5.361 0.629 3.827 5.428 6.391
beta_H[6,5] 8.789 0.628 7.856 8.653 10.240
beta_H[7,5] 6.745 0.347 6.067 6.738 7.443
beta_H[8,5] 8.215 0.237 7.868 8.193 8.698
beta_H[9,5] 8.205 0.468 7.284 8.214 9.104
beta_H[10,5] 10.086 0.232 9.619 10.084 10.541
beta_H[11,5] 11.541 0.226 11.086 11.544 11.980
beta_H[12,5] 8.478 0.196 8.103 8.477 8.881
beta_H[13,5] 10.010 0.132 9.755 10.011 10.270
beta_H[14,5] 9.196 0.236 8.762 9.185 9.671
beta_H[15,5] 11.173 0.248 10.674 11.180 11.641
beta_H[16,5] 9.945 0.162 9.621 9.950 10.255
beta_H[1,6] 10.187 0.196 9.847 10.170 10.631
beta_H[2,6] 11.516 0.106 11.311 11.514 11.734
beta_H[3,6] 10.813 0.162 10.471 10.819 11.115
beta_H[4,6] 12.870 0.822 11.151 12.882 14.403
beta_H[5,6] 5.954 0.615 4.777 5.933 7.201
beta_H[6,6] 8.736 0.667 6.978 8.858 9.713
beta_H[7,6] 9.889 0.575 8.718 9.898 11.027
beta_H[8,6] 9.502 0.315 8.937 9.530 9.944
beta_H[9,6] 8.474 0.765 7.016 8.458 10.016
beta_H[10,6] 9.515 0.316 8.844 9.547 10.068
beta_H[11,6] 10.799 0.351 10.051 10.815 11.428
beta_H[12,6] 9.383 0.263 8.881 9.377 9.914
beta_H[13,6] 11.055 0.158 10.779 11.046 11.379
beta_H[14,6] 9.871 0.288 9.312 9.875 10.423
beta_H[15,6] 10.866 0.433 10.020 10.870 11.700
beta_H[16,6] 10.567 0.207 10.106 10.583 10.946
beta_H[1,7] 10.904 0.883 8.774 11.013 12.376
beta_H[2,7] 12.215 0.420 11.332 12.222 13.045
beta_H[3,7] 10.540 0.662 9.042 10.598 11.655
beta_H[4,7] 2.515 4.173 -5.457 2.445 11.015
beta_H[5,7] 6.671 2.008 3.237 6.510 11.292
beta_H[6,7] 9.526 2.469 4.833 9.473 15.823
beta_H[7,7] 10.436 2.900 4.814 10.394 16.137
beta_H[8,7] 11.024 1.212 9.410 10.926 13.016
beta_H[9,7] 4.413 3.995 -3.832 4.466 12.235
beta_H[10,7] 9.804 1.466 7.120 9.711 13.004
beta_H[11,7] 11.002 1.724 7.894 10.875 14.768
beta_H[12,7] 10.032 0.945 8.073 10.096 11.591
beta_H[13,7] 11.678 0.744 9.893 11.764 12.877
beta_H[14,7] 10.503 0.959 8.486 10.569 12.106
beta_H[15,7] 12.158 2.289 7.716 12.124 16.641
beta_H[16,7] 11.991 1.063 10.272 11.806 14.517
beta0_H[1] 8.836 12.705 -16.791 8.811 35.667
beta0_H[2] 10.548 6.196 -2.663 10.644 22.822
beta0_H[3] 9.976 9.767 -9.547 9.828 30.116
beta0_H[4] 8.165 181.182 -354.258 3.741 374.026
beta0_H[5] 4.736 26.512 -47.074 4.655 53.865
beta0_H[6] 7.874 50.505 -93.249 7.633 113.893
beta0_H[7] 6.899 138.755 -261.374 6.078 280.372
beta0_H[8] 6.700 48.907 -20.232 6.432 29.046
beta0_H[9] 4.620 119.559 -248.480 7.204 245.931
beta0_H[10] 8.935 32.581 -59.926 9.718 72.068
beta0_H[11] 10.229 48.696 -97.371 10.515 115.131
beta0_H[12] 6.466 11.197 -16.121 6.811 27.645
beta0_H[13] 9.885 10.434 -10.858 9.842 30.729
beta0_H[14] 7.064 12.118 -14.906 6.921 29.797
beta0_H[15] 7.942 107.467 -208.581 6.326 225.688
beta0_H[16] 7.360 19.348 -31.180 8.098 43.772